The paper describes the effect of the addition of alumina nanofibers on the mechanical properties of the epoxy resin. Alumina nanofibers functionalized with epoxypropyl functional groups are used in this work. The dependence of the mechanical characteristics on the amount of the additive, as well as the features of its distribution in the material, is investigated. In the work, nanocomposites were obtained, which are epoxy resin with aluminum oxide nanofibers. The mechanical properties of the samples were studied by bending tests and differential mechanical analysis (DMA). It has been shown that the addition of alumina nanofibers leads to an increase in ultimate flexural strength. The maximum of this increase is near the percolation threshold of alumina nanofibers in epoxy resin. With the addition of 0.2% alumina nanofibers, the ultimate flexural strength increases from 41 to 71 MPa. It is shown that after exceeding the percolation threshold of nanofibers, the ultimate strength decreases. In this case, the elastic modulus increases from 0.643 to 0.862 GPa. DMA is shown that the glass transition temperature decreases with increasing amount of the additive. This indicates a decrease in the molecular weight of the polymer. By implication, this suggests that the hardener connects the epoxypropyl functional groups on the nanofibers and the epoxy groups in the resin, and as a result of this process, the nanofibers become natural polymer chain length limiters. The data obtained from mechanical testing and differential mechanical analysis can be used to strengthen epoxy resins in polymer composite materials and molding compositions.